1. Field of the Invention
This invention generally relates to data processing, and more particularly, to a method of smoothing data including noises and a data smoothing filter utilizing so-called fuzzy logic.
2. Description of the Prior Art
In a variety of measurements of physical quantities for controlling a machine which is used, for example, in the manufacturing industry, data obtained by such a measurement may be linearly distributed, if plotted on the x-y coordinates. For such linearly distributed data, a least squares method is employed for evaluating the linearity of a line constituted of the plotted data or points and deriving the angle formed by the line and the x-axis for predicting a future trend.
Among these n data points, if even one data point is located away from a straight line constituted of the remaining n-1 points, a statistical method such as the least squares method derives an angle different from an angle which would be derived based on the straight line constituted of the n-1 points.
Consider, for example, a case where a measurement has been made for a physical phenomenon to obtain n points which would have been linearly distributed, where n-1 points have been exactly measured to draw a straight line, however, only one point was disturbed by a noise and therefore plotted at a location away from the straight line. In this case, it would be correct to derive an angle formed by the x-axis and a straight line constituted of the n-1 points as the angle formed by the x-axis and a line constituted of measured data since the one point indicates erroneous data. A human can readily remove the exceptional point to select a correct angle and draw a straight line constituted of the remaining correct n-1 points.
The above-mentioned operation based on human judgement, however, is quite difficult to implement in known apparatus since such removal of exceptional points and selection of a correct angle are not a domain for machines. For example, if threshold values are provided for removing exceptional points, a slight difference (e.g. a small disturbance by noise) may result in large variation in derived straight lines and angles. Therefore, such straight lines and angles of data points derived by a conventional data processing apparatus tend to be different from human's sense. Although it is sometimes preferable to detect a straight line and measure an angle with human intuitive judgement, the prior art has not been able to carry out such human-like judgment by means of data processing apparatus.
As typically represented by a state observation of a system, e.g., a plant, a trend of the state and state transition of the system cannot be precisely predicted in many cases due to noises and probabilistic variations. However, as long as the mathematic model of the system is precisely described and the statistical characteristics of the noise has been analyzed, a state forecast may be carried out by means of a Karman filter. On the other hand, it is rather difficult or impossible to describe mathematic models for many existing systems, and a reliable state forecast, using a Karman filter, as mentioned above, will not be readily achieved.
More specifically, measured values, constantly disturbed by random noises as shown in FIG. 1, cannot be used for forecasting a state or state transition of a system. Conventionally, this type of measured data is analyzed by statistical techniques such as regression and moving average methods. In the case of large noises exceptionally present as shown in FIG. 2, conventional statistical techniques cannot provide highly reliable state forecasting. It is therefore necessary to employ another technique (e.g., differentiation) for removing such exceptional noises (spot noises). Thus, in conventional data processing, different techniques must be used for removing different kinds of noises. Thus, a single technique has not been able to appropriately process data including a plurality of kinds of noises.
As stated above, a human can readily remove exceptional points by subjective judgement to carry out a relatively highly reliable state forecasting. Full lines in FIGS. 1 and 2 respectively indicate an example of a smoothing performed by the inventor's subjective judgement for removing noises to estimate true data. Such data smoothing resulted from rather fuzzy knowledge and judgment for analyzing a graph of measured data. Although such knowledge and judgment do not provide precise state forecasting, such smoothed data may be important in effective data processing for displaying measured values of a system or performing a predictor control.